I love thinking of parabolas as being formed with a directrix and focus. Coming from a background in trajectory analysis, I find the abstract relationships of the curve to the point and line beautiful. When a light shines through the focus of a parabolic mirror, the light reflected is orthogonal to the directrix – WOW! Below is an interactive code to generate art by clicking to the right of the focus. I also created an animated version in the Gif above.
The code above led to the code below (and I would like to further expand this to a version with N-bounces of the beams of light). Click to clear the screen, and keep your mouse between the foci.